1. Chapter 17 Temperature, Thermal Expansion, and the Ideal Gas Law
17-2 Temperature and Thermometers
17-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics
17-4 Thermal Expansion
17-5 Thermal Stresses
17-6 The Gas Laws and Absolute Temperature
17-7 The Ideal Gas Law
17-8 Problem Solving with the Ideal Gas Law
17-9 Ideal Gas Law in Terms of Molecules: Avogadro’s Number

2. 17-2 Temperature and Thermometers
Temperature is a measure of how hot or cold something is.
Most materials expand when heated: An Iron beam is longer when hot than when cold
Concrete roads expand and
contract slightly with temperature
Figure Expansion joint on a bridge.
Expansion joint on a bridge

3. 17-2 Temperature and Thermometers
Thermometers are instruments designed to measure temperature. In order to do this, they take advantage of some property of matter that changes with temperature.
Early thermometers:
Built by Accademia del
Cimento ( ) in
Florence, Italy
Figure Thermometers built by the Accademia del Cimento (1657–1667) in Florence, Italy, are among the earliest known. These sensitive and exquisite instruments contained alcohol, sometimes colored, like many thermometers today.

4. 17-2 Temperature and Thermometers
Thermometers rely on expansion of material with temperature change.
Common thermometers used today include the liquid-in-glass type and the bimetallic strip.
Figure (a) Mercury- or alcohol-in-glass thermometer; (b) bimetallic strip.
Figure Photograph of a thermometer using a coiled bimetallic strip.

5. 17-2 Temperature and Thermometers
Figure Celsius and Fahrenheit scales compared.

6. 17-2 Temperature and Thermometers
Example 17-2: Taking your temperature.
Normal body temperature is 98.6°F. What is this on the Celsius scale?
Solution: Conversion gives 37.0 °C.

7. 17-2 Temperature and Thermometers
A constant-volume gas thermometer depends only on the properties of an ideal gas, which do not change over a wide variety of temperatures. Therefore, it is used to calibrate thermometers based on other materials.
Figure Constant-volume gas thermometer.

8. 17-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics
Two objects placed in thermal contact will eventually come to the same temperature. When they do, we say they are in thermal equilibrium.
The zeroth law of thermodynamics says that if two objects are each in equilibrium with a third object, they are also in thermal equilibrium with each other.

9. 17-4 Thermal Expansion
Linear expansion occurs when an object is heated.
Figure A thin rod of length l0 at temperature T0 is heated to a new uniform temperature T and acquires length l, where l = l0 + Δl.
Here, α is the coefficient of linear expansion.
T is the change in Temperature

10. 17-4 Thermal Expansion

11. 17-4 Thermal Expansion Example 17-3: Bridge expansion.
The steel bed of a suspension bridge is 200 m long at 20°C. If the extremes of temperature to which it might be exposed are -30°C to +40°C, how much will it contract and expand?
Solution: Substitution gives 4.8 cm expansion and 12 cm contraction.

12. 17-4 Thermal Expansion Example 17-5: Ring on a rod.
An iron ring is to fit snugly on a cylindrical iron rod. At 20°C, the diameter of the rod is cm and the inside diameter of the ring is cm. To slip over the rod, the ring must be slightly larger than the rod diameter by about cm. To what temperature must the ring be brought if its hole is to be large enough so it will slip over the rod?
Solution: The temperature needs to be raised by 430°C, to 450°C.

13. 17-4 Thermal Expansion
Conceptual Example 17-6: Opening a tight jar lid.
When the lid of a glass jar is tight, holding the lid under hot water for a short time will often make it easier to open. Why?
Solution: The lid will heat before the glass, and expand sooner. Also, metals generally expand more than glass for the same temperature difference.

14. 17-4 Thermal Expansion
Volume expansion is similar, except that it is relevant for liquids and gases as well as solids:
Here, β is the coefficient of volume expansion.
For uniform solids, β ≈ 3α.

15. 17-4 Thermal Expansion Example 17-7: Gas tank in the Sun.
The 70-liter (L) steel gas tank of a car is filled to the top with gasoline at 20°C. The car sits in the Sun and the tank reaches a temperature of 40°C (104°F). How much gasoline do you expect to overflow from the tank?
Solution: Both the tank and the gasoline expand; the amount that spills is the difference. However, the gasoline expands by about 1.3 L, whereas the tank expands by about 0.05 L – the expansion of the tank makes little difference.

16. 17-4 Thermal Expansion
Water behaves differently from most other solids—its minimum volume occurs when its temperature is 4°C. As it cools further, it expands, as anyone who leaves a bottle in the freezer to cool and then forgets about it can testify.
Figure 17-12: Behavior of water as a function of temperature near 4°C. (a) Volume of g of water, as a function of temperature. (b) Density vs. temperature. [Note the break in each axis.]

17. 17-5 Thermal Stresses
A material may be fixed at its ends and therefore be unable to expand when the temperature changes. It will then experience large compressive or tensile stress—thermal stress—when its temperature changes. The force required to keep the material from expanding is found from:
where E is the Young’s modulus of the material. Therefore, the stress is:

18. 17-6 The Gas Laws and Absolute Temperature
The relationship between the volume, pressure, temperature, and mass of a gas is called an equation of state.
We will deal here with gases that are not too dense.
Boyle’s law: the volume of a given amount of gas is inversely proportional to the pressure as long as the temperature is constant: PiVi=PfVf or:
Figure 17-13: Pressure vs. volume of a fixed amount of gas at a constant temperature, showing the inverse relationship as given by Boyle’s law: as the pressure decreases, the volume increases.

19. 17-6 The Gas Laws and Absolute Temperature
The volume is linearly proportional to the temperature, This is Charles’s Law: ViTf=VfTi
or:
as long as the temperature is somewhat above the condensation point and the pressure is constant. Extrapolating, the volume becomes zero at −273.15°C; this temperature is called absolute zero.
Figure Volume of a fixed amount of gas as a function of (a) Celsius temperature, and (b) Kelvin temperature, when the pressure is kept constant.

20. 17-6 The Gas Laws and Absolute Temperature